Mathematics/General Ability MCQs
Topic Notes: Mathematics/General Ability
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
51
A is 3 times as efficient as B and therefore takes 40 days less than B to complete a work. How many days will B alone take?
Answer:
60 days
Step 1: Efficiency ratio is 3:1. Time ratio is 1:3. Step 2: Difference in time parts is 3 - 1 = 2 parts. We are given 2 parts = 40 days, so 1 part = 20 days. Step 3: B takes 3 parts of time, which is 3 * 20 = 60 days.
52
A can do a work in 10 days, B in 12 days, and C in 15 days. They all start together, but A leaves after 2 days, and B leaves 3 days before completion. Total time taken is:
Answer:
7 days
Step 1: Total work = 60. A=6, B=5, C=4. All three work for first 2 days: 2*(15) = 30 units. Remaining = 30. Step 2: After A leaves, B and C work. B leaves 3 days before the end, so C works alone for the last 3 days: 3*4=12 units. Remaining = 30 - 12 = 18. Step 3: These 18 units were done by B and C together. Time = 18/(5+4) = 2 days. Total time = 2 (all) + 2 (B+C) + 3 (C alone) = 7 days.
53
A does 4/5 of a piece of work in 20 days. He then calls in B and they finish the remaining work in 3 days. How long would B alone take to do the whole work?
Answer:
37.5 days
Step 1: A's total time = 20 * (5/4) = 25 days. The remaining work is 1/5. Step 2: A and B do 1/5 of the work in 3 days, so A+B's total time = 15 days. Step 3: Let Total work = 75. A's eff = 3, A+B's eff = 5. B's eff = 2. Time for B alone = 75 / 2 = 37.5 days.
54
X can complete 1/4 of a job in 3 days, and Y can complete 1/6 of it in 4 days. How long will it take them to complete the job together?
Answer:
8 days
Step 1: X's total time = 3 * 4 = 12 days. Y's total time = 4 * 6 = 24 days. Step 2: Total work = LCM(12, 24) = 24. X's eff = 2, Y's eff = 1. Step 3: Combined eff = 3. Time taken = 24 / 3 = 8 days.
55
A can do 1/2 of a work in 5 days, and B can do 1/3 of the work in 4 days. How many days will they take working together?
Answer:
5.45 days
Step 1: A's time for full work = 5 * 2 = 10 days. B's time for full work = 4 * 3 = 12 days. Step 2: Total work = LCM(10, 12) = 60. A's eff = 6, B's eff = 5. Step 3: Combined efficiency = 11. Time = 60 / 11 = 5.45 days.
56
A and B can finish a task in 8 days, B and C in 12 days, C and A in 24 days. How many days will A alone take?
Answer:
24 days
Step 1: LCM(8, 12, 24) = 24. A+B=3, B+C=2, C+A=1. Step 2: 2(A+B+C) = 6, so A+B+C = 3. Step 3: A's efficiency = (A+B+C) - (B+C) = 3 - 2 = 1. A alone takes 24 / 1 = 24 days.
57
A and B can do a job in 10 days, B and C in 15 days, and C and A in 18 days. Working together, in how many days will they finish?
Answer:
9 days
Step 1: LCM(10, 15, 18) = 90. A+B=9, B+C=6, C+A=5. Step 2: 2(A+B+C) = 9+6+5 = 20. Therefore, A+B+C = 10. Step 3: Time taken together = 90 / 10 = 9 days.
58
A and B can do a work in 12 days, B and C in 15 days, and C and A in 20 days. How long will A, B, and C take to finish it together?
Answer:
10 days
Step 1: Total work = LCM(12, 15, 20) = 60. Efficiencies: A+B=5, B+C=4, C+A=3. Step 2: Sum of efficiencies: 2(A+B+C) = 5+4+3 = 12, so A+B+C = 6. Step 3: Time taken by all three together = 60 / 6 = 10 days.
59
A can do a work in 15 days and B in 20 days. With the help of C, they complete the work in 6 days and receive $400. What is C's share?
Answer:
$120
Step 1: Work done by A in 6 days = 6/15 = 2/5. Work done by B in 6 days = 6/20 = 3/10. Step 2: Total work by A and B = 4/10 + 3/10 = 7/10. So, C's work = 3/10. Step 3: C's share = (3/10) * $400 = $120.
60
A, B, and C undertake to do a job for $600. A and C together complete 3/5 of the work. What is B's share?
Answer:
$240
Step 1: The portion of work done by A and C together is 3/5. Step 2: Therefore, B completes the rest, which is 1 - 3/5 = 2/5 of the work. Step 3: B's share = (2/5) * $600 = $240.